Find the mean of the following frequency distribution using a sui… - Vidyadip

Question

Find the mean of the following frequency distribution using a suitable method.

Class	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$25$	$40$	$42$	$33$	$10$

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Answer

Class interval	Frequency $f_i$	Mid-value $x_i$	$\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_\text{i}-203.5}{1}$	$f_i \times u_i$
$20-30$	$25$	$25$	$-20$	$-500$
$30-40$	$40$	$35$	$-10$	$-400$
$40-50$	$42$	$45 = A$	$0$	$0$
$50-60$	$33$	$55$	$10$	$330$
$60-70$	$10$	$65$	$20$	$200$
	$\sum\text{f}_\text{i}=150$			$\sum\text{f}_\text{i}\text{u}_\text{i}=-370$

Thus, $\text{A}=45,\ \sum\text{f}_\text{i}=150$ and $\sum\text{f}_\text{i}\text{u}_\text{i}=-370$
Mean $=\text{A}+\Big\{\text{h}\times\frac{\sum\text{f}_\text{i}\text{u}_\text{i}}{\sum\text{f}_\text{i}}\Big\}$
$45+\frac{(-370)}{150}$
$=45-2.47$
$=42.53$

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